Chọn phương án C.

\(\begin{aligned}
\displaystyle\int\limits_0^1\dfrac{2x^2+3x+1}{2x+3}\mathrm{\,d}x&=\int\limits_0^1\left(x+\dfrac{1}{2x+3}\right)\mathrm{\,d}x\\
&=\left(\dfrac{x^2}{2}+\dfrac{1}{2}\ln|2x+3|\right)\bigg|_0^1\\
&=\dfrac{1}{2}+\dfrac{1}{2}\ln5-\dfrac{1}{2}\ln3.
\end{aligned}\)

Theo đó  \(a=\dfrac{1}{2},\,b=-\dfrac{1}{2},\,c=\dfrac{1}{2}\).
Suy ra \(T=1\).